Novel windowed linear canonical transform: Definition, properties and application

Linear canonical transform (LCT) has emerged as a powerful tool in nonstationary signal processing. However, it fails to reveal the information of local frequency varying with time due to the global kernel function. In this paper, a novel windowed linear canonical transform (NWLCT) is presented to give a clear time-frequency representation for time-varying signals. Firstly, the definition of NWLCT is proposed by a generalized convolution operator not a sliding window. Some basic properties of NWLCT are derived, such as inverse transform, Parseval theorem and reproducing kernel. Moreover, time-frequency resolution of NWLCT is analyzed theoretically, and the optimal window is derived. Finally, the applications of NWLCT in local spectral analysis for linear frequency modulated (LFM) signals are offered, including mono-and multi-component signals with similar local features. Theoretical and simulation results demonstrate that the proposed NWLCT preserves a crucial physical interpretation similar to classical short-time Fourier transform, which extends low-pass filter banks in the LCT domain. Compared with other time-frequency methods, NWLCT outperforms in improving the energy concentration and being robust to noise in terms of LFM signal processing.(c) 2022 Elsevier Inc. All rights reserved.